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Mint temperaments

Edit 0 17 …
Progression | Ripple | Smate | Hemismate | Subklei | Slurpee
These are low complexity, high error temperaments tempering out the septimal quarter-tone, 36/35. 36 is both a square and a triangular number, and this helps make 36/35 a septimal interval of considerable significance. Temperaments tempering it out include beep, dicot, dominant, father, diminished, august, hystrix, penta, hexadecimal, ripple and gorgo.

Progression

Comma: 3456/3125

POTE generator: ~25/24 = 140.995

Map: [<1 1 2|, <0 5 3|]
EDOs: 8, 9, 17c
Badness: 0.2005

7-limit

Commas: 36/35, 392/375

POTE generator: ~15/14 = 140.927

Map: [<1 1 2 2|, <0 5 3 7|]
Wedgie: <<5 3 7 -7 -3 8||
EDOs: 9, 17c
Badness: 0.0484

11-limit

Commas: 36/35, 56/55, 77/75

POTE generator: ~15/14 = 140.747

Map: [<1 1 2 2 3|, <0 5 3 7 4|]
EDOs: 8, 9, 17
Badness: 0.0261

13-limit

Commas: 26/25, 36/35, 56/55, 66/65

POTE generator: ~15/14 = 140.751

Map: Map: [<1 1 2 2 3 3|, <0 5 3 7 4 6|]
EDOs: 8, 9, 17
Badness: 0.0182

17-limit

Commas: 26/25, 36/35, 51/50, 56/55, 66/65

POTE generator: ~15/14 = 141.404

Map: [<1 1 2 2 3 3 4|, <0 5 3 7 4 6 1|]
EDOs: 8, 9, 17
Badness: 0.0167

19-limit

Commas: 26/25, 36/35, 51/50, 56/55, 57/55, 66/65

POTE generator: ~15/14 = 140.479

Map: [<1 1 2 2 3 3 4 4|, <0 5 3 7 4 6 1 2|]
EDOs: 8, 9, 17, 94
Badness: 0.0168

Ripple

Comma: 6561/6250

POTE generator: ~27/25 = 100.838

Map: [<1 2 3|, <0 -5 -8|]
EDOs: 12, 71b, 83b, 95b, 107bc, 119bc
Badness: 0.1389

7-limit

Commas: 36/35, 2560/2401

POTE generator: ~21/20 = 99.483

Map: [<1 2 3 3|, <0 -5 -8 -2|]
Wedgie: <<5 8 2 1 -11 -18||
EDOs: 12, 23
Badness: 0.0597

11-limit

Commas: 36/35, 80/77, 126/121

POTE generator: ~21/20 = ~12/11 = 99.385

Map: [<1 2 3 3 4|, <0 -5 -8 -2 -6|]
EDOs: 12
Badness: 0.0388

13-limit

Commas: 36/35, 40/39, 66/65, 147/143

POTE generator: ~21/20 = ~12/11 = ~14/13 = 98.572

Map: [<1 2 3 3 4 4|, <0 -5 -8 -2 -6 -3|]
EDOs: 12f
Badness: 0.0316

Smate

Comma: 2048/1875

POTE generator: ~5/4 = 420.855

Map: [<1 3 2|, <0 -4 1|]
EDOs: 11, 14, 17c, 20c, 37c
Badness: 0.179

7-limit

Commas: 36/35, 2048/1875

POTE generator: ~5/4 = 422.275

Map: [<1 3 2 6|, <0 -4 1 -9|]
Wedgie: <<4 -1 9 -11 3 24||
EDOs: 14, 17c, 37cd
Badness: 0.0779

11-limit

Commas: 36/35 56/55 243/242

POTE generator: ~5/4 = 422.217

Map: [<1 3 2 6 7|, <0 -4 1 -9 -10|]
EDOs: 14, 17c, 37cde
Badness: 0.0425

13-limit

Commas: 26/25, 36/35, 56/55, 243/242

POTE generator: ~5/4 = 423.020

Map: [<1 3 2 6 7 3|, <0 -4 1 -9 -10 2|]
EDOs: 14, 17c
Badness: 0.0368

Hemismate

commas: 256/245, 392/375

POTE generator: ~8/7 = 210.452

Map: [<1 3 2 3|, <0 -8 2 -1|]
Wedgie: <<8 -2 1 -22 -21 8||
EDOs: 6, 11, 17c, 40bcd
Badness: 0.1543

11-limit

Commas: 56/55, 77/75, 256/245

POTE generator: ~8/7 = 210.481

Map: [<1 3 2 3 4|, <0 -8 2 -1 -3|]
EDOs: 6, 11, 17c, 40bcde
Badness: 0.0655

13-limit

Commas: 26/25, 56/55, 77/75, 256/245

POTE generator: ~8/7 = 210.974

Map: [<1 3 2 3 4 3|, <0 -8 2 -1 -3 4|]
EDOs: 6, 11, 17c
Badness: 0.0505

Subklei

Comma: 17496/15625

POTE generator: ~6/5 = 284.293

Map: [<1 3 4|, <0 -6 -7|]
EDOs: 4, 17c, 21, 38c
Badness: 0.3559

7-limit

Commas: 36/35, 1029/1000

POTE generator: ~6/5 = 284.219

Map: [<1 3 4 4|, <0 -6 -7 -5|]
Wedgie: <<6 7 5 -3 -9 -8||
EDOs: 4, 17c, 21, 38c
Badness: 0.0611

11-limit

Commas: 36/35, 77/75, 352/343

POTE generator: ~6/5 = 283.253

Map: [<1 3 4 4 7|, <0 -6 -7 -5 -15|]
EDOs: 17c, 55cd
Badness: 0.0447

Subkla

Commas: 36/35, 56/55, 1029/1000

POTE generator: ~6/5 = 283.822

Map: [<1 3 4 4 3|, <0 -6 -7 -5 2|]
EDOs: 4, 17c, 21, 38ce, 55cde
Badness: 0.0472

13-limit

Commas: 36/35, 56/55, 66/65, 640/637

POTE generator: ~6/5 = 283.882

Map: [<1 3 4 4 3 3|, <0 -6 -7 -5 2 3|]
EDOs: 4, 17c, 21, 38ce, 55cde
Badness: 0.0367

13-limit

Commas: 26/25, 36/35, 66/65, 352/343

POTE generator: ~6/5 = 282.856

Map: [<1 3 4 4 7 7|, <0 -6 -7 -5 -15 -14|]
EDOs: 17c
Badness: 0.0323

Slurpee

Comma: 177147/156250

POTE generator: ~27/25 = 72.742

Map: [<1 2 3|, <0 -7 -11|]
EDOs: 16, 17c, 33
Badness: 0.6893

7-limit

Commas: 36/35, 51200/50421

POTE generator: ~21/20 = 72.303

Map: [<1 2 3 3|, <0 -7 -11 -3|]
Wedgie: <<7 11 3 1 -15 -24||
EDOs: 16, 17c, 33, 50cd, 83bcd
Badness: 0.1149

11-limit

Commas: 36/35, 121/120, 352/343

POTE generator: ~21/20 = 72.297

Map: [<1 2 3 3 4|, <0 -7 -11 -3 -9|]
EDOs: 16, 17c, 33, 50cd, 83bcd
Badness: 0.0505

13-limit

Commas: 36/35. 66/65, 143/140, 352/343

POTE generator: ~21/20 = 72.409

Map: [<1 2 3 3 4 4|, <0 -7 -11 -3 -9 -5|]
EDOs: 16, 17c, 33, 83bcd
Badness: 0.0331